HOMEWORK 5
DUE MONDAY, JUNE 23
Wednesday, June 19
• §6.1 # 3, 16, 24
• §6.2 # 3, 5, 15, 22
Thursday, June 20
• §6.3 # 3, 9, 21
• §6.4 # 1, 3, 9 part (a) only, 11.
• §6.5 #2, 9 part (a) only, 11.
Problem 1. The goal of this problem is to look briefly at the phenomenon of resonance
and beats. Consider the initial value problem
y 00 + y = f (t),
y(0) = 0, y 0 (0) = 0
where f (t) = (1 − u 13π (t)) cos(3t) + u 13π (t) cos(t).
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(a) Graph the function f (t).
(b) Solve the initial value problem.
(c) (optional, but recommended!) Graph the solution. You can try to do this
by hand, or you can use a computer program. Macintosh computers come with a
graphing utility called “Grapher”. For PC users there is a freeware program called
“GraphCalc”. Mostly, you should draw a graph for the solution for 0 < t < 13π/2,
and, say 7π < t. How does the qualitative behaviour of the solution change after
t = 13π/2? What happens to the amplitude after t = 7π?
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